Promotor: J. Zaanen
|Links||Thesis in Leiden Repository|
As crystals are classified by space groups, nematic liquid crystals should be in principle classified by point groups. Conventionally, the study of nematic liquid crystals has mainly been focused on a very small subset of the whole nematic family, partly because of limitations of traditional methods. In this thesis, we introduce a non-Abelian gauge theory that can treat nematic phases with arbitrary point group symmetries in a unified framework in an efficient way. The proposed gauge theory allows us to compare nematic phases against a common reference. We are therefore able to quantify the orientational fluctuations of nematic orders with different symmetries and identify a novel chiral liquid phase. Moreover, this gauge theory can act as an order-parameter generator, and we thus achieve a full classification of nematic-order-parameter tensors, which has never been done before. Finally, we show that the gauge theory provides a convenient way to access the anisotropy of axial orders, by which we generalize the extensively studied biaxial-uniaxial transition of D2h nematics to a much broader class.